Andrew Judge, 32, from Greenock was last seen at around 11.50am on Wednesday in the town's Dunlop Street.
He was reported missing by his mother on Monday.
Andrew is described as 5ft 8in, heavy built with short sandy coloured hair.
When last seen, he was wearing a black hooded jacket, black tracksuit and boots.
Police said he is known to frequent the Central Library, McLean Museum, Greenock Town Centre and Oakmall Shopping Centre.
Inspector Cassie Glass, said: "Due to the passage of time, we are becoming increasingly concerned for his safety and wellbeing.
"Andrew has some health issues and it is vital that we trace him as soon as possible to ensure that he is okay.
"He has not been reported missing before.
"I would urge anyone who has seen him, or has any information regarding his whereabouts, to contact police."
Anyone with any information is asked to contact Greenock Police on 101.